FIRST YEAR STUDENTS' MATHEMATICS LEARNING ... - Eric

11 downloads 813 Views 260KB Size Report
Ciarán Mac an Bhaird received his PhD in mathematics from National University ... at the Mathematics Support Centre (MSC); and homework submission rates.
Nguyen, T.T. and Trimarachi, A. (2010). “Active learning in introductory economics: do MyEconLab and Aplia make any difference?” International Journal for the Scholarship of Teaching and Learning, vol. 4, no. 1, pp. 1-18. O’Dea, W.P. and Ring, D.W. (2008). “The impact of Aplia on student performance in intermediate microeconomics theory,” Unpublished. Division of Economics and Business, SUNYOneonta. Turley, G., Moloney, M. and O’Toole, F. (2006). Principles of Economics: An Irish Textbook. Dublin: Gill and Macmillan.

FIRST YEAR STUDENTS’ MATHEMATICS LEARNING EXPERIENCES AT THE NATIONAL UNIVERSITY OF IRELAND MAYNOOTH Contributors: Ciarán Mac an Bhaird and Ann O’Shea, Department of Mathematics, National University of Ireland Maynooth Biographical Note Ciarán Mac an Bhaird received his PhD in mathematics from National University of Ireland (NUI) Maynooth. He has been manager of the Mathematics Support Centre and a lecturer in mathematics there since 2007. He is a committee member of the Irish Mathematics Support Network and conducts research in mathematics education and algebraic number theory. Ann O’Shea holds a PhD in mathematics from the University of Notre Dame, USA. She has been a lecturer in the mathematics department at NUI Maynooth since 1992, and is currently the Director of the Mathematics Support Centre. She conducts research in the area of mathematics education. ABSTRACT This paper considers the factors that impact on student success in first year science mathematics courses at the National University of Ireland Maynooth (NUI Maynooth). These factors include previous performance in the subject, attendance at lectures and tutorials, the number of assignments submitted, and attendance at the Mathematics Support Centre (MSC). The results of this initial study will be used to identify behaviour patterns that lead to successful completion of first year courses. The findings will help mathematics departments to target support initiatives in areas which are most likely to improve student learning. INTRODUCTION AND RATIONALE FOR THE PROJECT The aim of this research is to determine the factors that impact on assessment grades in a first year mathematics course for science students. The factors that we will consider are: Irish secondary school Leaving Certificate (LC) grades in mathematics; diagnostic test scores; tutorial and lecture attendance; attendance at the Mathematics Support Centre (MSC); and homework submission rates. The motivation for this study is twofold. Firstly we would like to be able to identify students who are at risk of failing, so that we can offer them timely and appropriate support. Secondly, we would like to know whether the supports offered by the mathematics department at NUI Maynooth are successful. The department invests a lot of its resources in providing student support, and many of these resources are targeted at first year students. This is true of most mathematics departments in Ireland, and the last few years have seen an increase in the supports available. It seems sensible therefore to try to determine the most successful types of support. Many Irish third level institutions have opened mathematics support or learning centres over the last ten years (Gill et al, 2008). The MSC at NUI Maynooth opened in the academic year 2007/08. It operates as a drop-in centre which is open for eighteen hours per week for twenty-four weeks of the year. It is staffed by a manager and a group of experienced tutors. In its first year of operation, there were 2493 visits by 273 students. In its second year, these numbers increased to 4647 visits by 509 students. Research on the centre at NUI Maynooth (Mac an Bhaird et al, 2009) has shown that students who attend have a higher probability of succeeding in mathematics modules than those who do not attend. Similar results have been found in studies of other support centres (Croft, 2008).

122

NATIONAL ACADEMY THIRD ANNUAL CONFERENCE

123

Of course, support centres are not the only resource available to students and are not the only factor determining success. In a study of first year engineering students at Loughborough University, Symonds (2008) showed that lecture and tutorial attendance, diagnostic test results, as well as mathematics support centre attendance were significant predictors of success in mathematics modules. At the University of Limerick, Liston and O’Donoghue (2009) found that success was related to affective variables such as attitude to mathematics, enjoyment of mathematics, and mathematics self-concept. Their study also reported that measures of previous mathematical achievement such as Leaving Certificate grades and diagnostic test results were good predictors of final examination scores. THE STUDY GROUP This paper investigates the effect of a number of variables on the mathematics grades of the first year science class at NUI Maynooth for the year 2008/09. It considers the 267 students who sat the summer examinations. Of these students, 35% had taken higher level mathematics at Leaving Certificate, 63% had taken ordinary level mathematics and 2% had not taken the Leaving Certificate examination. Mathematics is a compulsory subject for these students and only about 10% wish to study the subject to degree level. METHODOLOGY A diagnostic test is administered to all first year mathematics students during their first week in the university. The test assesses basic mathematical skills, and the department uses the results to identify students with weak mathematical backgrounds. These students are offered additional help in the form of an online course and a weekly workshop. In the year 2008/09, 27% of the class were deemed to be at-risk of failing first year mathematics. Each first year mathematics student is assigned to a small group tutorial. These tutorial groups meet twenty times in the academic year and attendance is recorded by the tutor. Students are required to submit a weekly assignment which is graded by the tutor. These assignments count for 25% of the module marks. Over the course of the year, the students study four mathematics modules. In the year 2008/09, lecture attendance at one of these modules was recorded by the lecturer. This module was on integral calculus and is considered the most difficult of the first year modules. Students were asked to inform us of their Leaving Certificate results during the first week of term. The final first year subject marks were obtained from the departmental administration. Attendance at the MSC is recorded by a dedicated staff member, and all figures are compiled by the MSC manager. RESULTS The median number of tutorials attended by students was fifteen (out of twenty). Approximately 22% of students missed no more than one tutorial. The median number of lectures attended was sixteen (out of twenty-four). The majority of students handed in most of their assignments. The median number of assignments submitted was 17.5 (out of twenty) and 18% submitted all assignments. Almost 61% of the group attended the MSC at least once, and of these 84% returned. A regression analysis, a common statistical tool, was carried out with the final subject mark (out of 1000) as the dependent variable and with Leaving Certificate mathematics points (LC points), Leaving Certificate mathematics level (LC level), diagnostic test results,

124

lecture attendance, tutorial attendance, number of assignments submitted, and MSC attendance as independent variables. Table 1 shows the Pearson correlations between these variables. (Here * denotes that the correlation is significant at the 0.05 level). Table 1: Table of Pearson Correlations

Final Mark LC Points Diagnostic Test

LC Points

Diagnostic Test

Lecture Attendance

Tutorial Attendance

Assignments Submitted

MSC Attendance

0.68*

0.6*

0.4*

0.48*

0.64*

0.26*

1

0.73*

0.05

0.14*

0.26*

-0.08

1

-0.003

0.11

0.25*

-0.16*

1

0.55*

0.59*

0.34*

1

0.74*

0.32*

1

0.28*

Lecture Attendance Tutorial Attendance Assignments Submitted

All of our independent variables are positively and significantly correlated with the final subject mark. The diagnostic test results and the LC points are highly correlated. This is not surprising since both of these variables measure students’ mathematical background. Both of these variables are negatively correlated with attendance at the MSC. It may be that students with a strong mathematical background have fewer problems in first year mathematics modules and therefore visit the MSC less often than those who are struggling. A stepwise regression was carried out and the predictors in the final model were LC points and level, diagnostic test results, MSC attendance, and number of assignments submitted. The model excluded the number of tutorials and lectures attended. The R-square for this model was 0.772, which suggests that the model variables account for 77% of the variance in the final subject mark. The regression equation is: Final Mark = -89.79 +3.195 (LC Points) +84.106 (LC Level) +2.51 (Diagnostic test) + 19.108 (Assignments submitted) +6.144 (Attendance at MSC). Note that LC Level was coded 0 for students who had studied mathematics at ordinary level and 1 for higher level. From this equation, we can see that if all other variables are held constant then a student with higher level mathematics at Leaving Certificate would be expected to score eighty-four marks out of 1000 more than an ordinary level student. It also seems that each visit to the MSC adds six marks out of 1000 to the student’s final mark and each assignment adds nineteen marks. CONCLUSIONS The mathematics department provides learning support to students both through its tutorial and homework assignment system, and through the Mathematics Support centre (MSC). From our study, we can see that these resources are being used by the first Science group. Indeed attendance at tutorials and lectures is relatively high when compared with other similar studies (for example Kirby and McElroy, 2003). Attendance at the MSC is considered good, with 61% of our group attending at

NATIONAL ACADEMY THIRD ANNUAL CONFERENCE

125

least once. This figure was dramatically up from 32% the previous year.

FORGING RESEARCH-TEACHING LINKAGES THROUGH ACTION RESEARCH: AN EXAMPLE OF FACILITATING THE DEVELOPMENT OF COMPETENCY IN CRITICAL REFLECTION

Our regression model showed us that the significant predictors of success could be divided into two groups: mathematical background (LC level, LC points and diagnostic test result); and measures of student engagement (number of assignments submitted and number of visits to the MSC). Since attendance at the MSC is purely voluntary, the number of visits can be thought of as a measure of a student’s engagement and effort. Unlike studies carried out by Symonds (2008) and Kirby and McElroy (2003), our model did not include lecture and tutorial attendance as significant predictors of final grade. This does not mean that attendance at lectures or tutorials is unimportant. Recall from Table 1 that these variables are highly correlated with the number of assignments submitted and the number of visits to the MSC, and this may be the reason why the final model did not include them. It may be that the experience of attending a lecture or tutorial is a passive one for some students. The lecture group is very large and this makes it difficult for lecturers to foster active learning. On the other hand, working on an assignment or visiting the MSC requires the student to take responsibility for their own learning. This act of taking personal responsibility is vital in our opinion.

Contributor: Catherine Lowry-O’Neill, Waterford Institute of Technology

Our study leads us to believe that in order to identify at-risk students we need to look not only at the students’ past mathematical achievement but also at their level of engagement with the subject. The results also suggest that supports that foster active rather than passive learning are beneficial. We plan to carry out a further analysis of our data to refine our model and we are in the process of interviewing students in an effort to ascertain which supports help them the most.

ABSTRACT Action research is an approach to enquiry that forges linkages between research and teaching, with each potentially informing the other in a responsive and creative cycle. This paper provides an overview of a pedagogic action research project which was undertaken in order to respond directly to learning needs expressed by a group of second year students on a Masters programme in Learning and Teaching.

REFERENCES Croft, T. (2008) Measuring the Effectiveness of Support Centres [online]. Loughborough: Mathcentre. Available from: http://www.mathcentre.ac.uk/courses/mathematicssupport-centre/measuring_effectivess/ [accessed 2 July 2010]. Gill, O., O’Donoghue, J., and Johnson P. (2008). Mathematics Support Provision in Irish Third Level Institutions. Limerick: Regional Centre for Excellence in Mathematics Teaching and Learning. Kirby, A. and McElroy, B. (2003). “The effect of attendance on grade for first year economics students in University College Cork”, The Economic and Social Review, vol. 34, no. 3, pp. 311-326. Liston, M. and O’Donoghue, J. (2009). “Factors influencing the transition to university service mathematics: part 1 a quantitative study”, Teaching Mathematics and its Applications, vol. 28, no. 2, pp. 77-87. Mac an Bhaird, C., Morgan, T., and O’Shea, A. (2009). “The impact of the mathematics support centre on the grades of first year students at the National University of Ireland Maynooth”, Teaching Mathematics and its Applications, vol. 28, no. 3, pp. 117-122. Symonds, R. (2008). Evaluating Students Engagement with Mathematics Support, PhD Thesis: Loughborough University.

126

Biographical Note Catherine Lowry-O’Neill graduated with a BA and DPhil from the University of Ulster at Coleraine (UUC). She lectured in French in UUC, the University of Limerick, and the University of Leeds before arriving in Waterford Institute of Technology (WIT) in 1997. Catherine was invited to join the team in the School of Education and Professional Development in 2005 and has subsequently graduated with an MA in Management in Education. She currently lectures on the MA in Learning and Teaching and her research interests include emotional intelligence and reflective practice. KEYWORDS Reflection; action research; integrative reflection; template.

An espoused aim of the MA programme is to facilitate the enhancement of the students’ competency in reflective practice. This paper outlines the process that took place when learners openly communicated some difficulties they had in this regard, in particular when faced with the challenge of writing their reflections in a manner that consistently demonstrated a capacity to be critical. It adumbrates the two specific actions that were taken within the context of the living theories approach to action research – the use of Socratic questioning and the development of a new approach to reflective writing – with a focus on the latter. The living theories approach to action research begins with the question, ‘How do I improve my practice?’ (Whitehead, 1989) and involves the practitioner seeking out ways in which to influence her own learning and that of others. By interacting with the students in a collaborative process, there is a possibility of creating new knowledge individually and collectively (Whitehead and McNiff, 2006). The outcomes of the project, including the effect of the pedagogic initiatives on student learning, and the development of a new framework for reflective writing - the ‘Integrative Reflection Template’ – are also presented, with the on - going nature of the process of enquiry made explicit. INTRODUCTION Reflection is undoubtedly a complex process (Dewey, 1933; Boud, 1985; Cowan, 1998). It requires, for instance, mental effort, critical self-analysis, and openness to the idea that one’s perceptions may be flawed or distorted. Nonetheless, its potential benefits in terms of nurturing the development of professionalism and expertise (Schon, 1984) has meant that the competency has become increasingly integrated into curricula in disciplines such as nurse education, business studies, and teacher education. Still, given the complexity of the approach, it is unsurprising that students may experience genuine challenge in developing their competencies in this regard.

NATIONAL ACADEMY THIRD ANNUAL CONFERENCE

127